0 does not have a multiplicative inverse. Further ,such is an inherent property of any field .
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Everything but zero.
0
0. By the definition of "additive inverse", the sum of ANY number and its additive inverse must be 0.
When a number is added to its additive inverse, the result is always 0.
The sum of a number and its inverse is 0, because that's what "its inverse" means. Inverse is whatever you need to use to "undo" the operation. For example, (2)+(-2)=0. If you go forward 2, then backward 2, you are where you started.